# Velocity distribution

1. Jan 14, 2006

### JSBeckton

I'm struggling with a fluid mechanics problem:
Viscosity at 15 degrees C = 1.114x10^-3
What direction should I be going in here? Do I need to use the velocity equation to solve for U and then find the force with a different equation?
Thanks for any help.

2. Jan 18, 2006

### jaap de vries

Assuming the flow is fully developed which it seems to be judging by the 1-D equation you gave the shear stress at the wall is simply

tau = mu du/dy, (evaluated a y = -0.5*h)

where mu is the viscosity.

du/dy = Umax*(8y/h^2), which becomes -8/2h= Umax*(-4/h) = 0.005*(-4/0.001) = -20

times the viscosity this becomes,

1.114*10^-3*-20 = -22.28 N/m^2

Since the area is 1 m^2 the net force of the plate on the fluid is 22.28 [N] in the negative x-direction

I hope this was of any help. I am pretty sure you have to use the velocity gradient at the bottom location. I am tired so I may have made a mistake but the principle should be pretty clear

Jaap

Last edited: Jan 18, 2006
3. Jan 19, 2006

### JSBeckton

Thanks, it helped.